Determine if Odd, Even, or Neither f(x)=sin(2x)

Problem

ƒ(x)=sin(2*x)

Solution

1. Recall the definitions of even and odd functions. A function is even if ƒ*(−x)=ƒ(x) and odd if ƒ*(−x)=−ƒ(x)

2. Substitute −x into the function for every instance of x

ƒ*(−x)=sin(2*(−x))

3. Simplify the expression inside the sine function.

ƒ*(−x)=sin(−2*x)

4. Apply the odd identity for the sine function, which states that sin(−θ)=−sin(θ)

ƒ*(−x)=−sin(2*x)

5. Compare the result to the original function. Since ƒ*(−x)=−ƒ(x) the function is odd.

Final Answer

ƒ(x)=sin(2*x)* is Odd

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